~

codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/homological_product.yml

@@ -42,11 +42,9 @@ features:
     - 'Parallel Pauli product measurements via homomorphic CNOT gates \cite{arxiv:2407.18490}.'
   fault_tolerance:
     - 'Universal set of gates can be obtained by fault-tolerantly mapping between different encoded representations of a given logical state \cite{arxiv:1807.09783}.'
-    - 'Single-ancilla syndrome extraction circuits do not admit \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:2409.02193}.'
 
   decoders:
     - 'Union-find \cite{arxiv:2009.14226}.'
-    - 'Single-ancilla syndrome extraction circuits do not admit \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:2409.02193}.'
 
 relations:
   parents:

codes/quantum/qubits/stabilizer/qldpc/homological/balanced_product/hypergraph_product.yml

@@ -41,6 +41,7 @@ features:
     - 'Hadamard (up to logical SWAP gates) and control-\(Z\) on all logical qubits \cite{arxiv:2204.10812}.'
     - 'Patch-transversal gates inherited from the automorphism group of the underlying classical codes \cite[Appx. D]{arxiv:2309.11719}.'
   decoders:
+    - 'Single-ancilla syndrome extraction circuits do not admit \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:2409.02193}.'
     - 'ReShape decoder that uses minimum weight decoders for the classical codes used in the hypergraph construction \cite{arxiv:2105.02370}.'
     - '2D geometrically local syndrome extraction circuits with depth \hyperref[topic:asymptotics]{order} \(O(\sqrt{n})\) using \hyperref[topic:asymptotics]{order} \(O(n)\) ancilla qubits \cite{arxiv:2109.14599}.'
     - 'Improved BP-OSD decoder \cite{arxiv:2206.03122}.'
@@ -52,6 +53,8 @@ features:
   code_capacity_threshold:
     - 'Some thresholds were determined in Ref. \cite{arxiv:1208.2317}.'
     - 'Bounds on code capacity thresholds using ML decoding can be obtained by mapping the effect of noise on the code to a statistical mechanical model \cite{arxiv:1804.01950}. For example, a threshold of \(7\%\) was obtained under independent \(X\) and \(Z\) noise for codes obtained from random \((3,4)\)-regular Gallager codes.'
+  fault_tolerance:
+    - 'Single-ancilla syndrome extraction circuits do not admit \hyperref[topic:effective-distance]{hook errors} \cite{arxiv:2409.02193}.'
   threshold:
     - 'Circuit-level noise: \(0.1\%\) with all-to-all connected syndrome extraction circuits \cite{arxiv:2109.14599} and DiVincenzo-Aliferis syndrome extraction circuits \cite{arxiv:quant-ph/0607047} combined with non-local gates \cite{arxiv:2409.05818}.
     No threshold observed above physical noise rates at or above \(10^{-6}\) using 2D geometrically local syndrome extraction circuits.'

codes/quantum/qubits/stabilizer/topological/color/3d_color/stab_15_1_3.yml

@@ -56,7 +56,7 @@ relations:
     - code_id: doubled_color
       detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}.'
     - code_id: steane
-      detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}. A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[15,1,3]]\) code \cite{arxiv:1304.3709,arxiv:1403.2734,arxiv:1703.03860,arxiv:2210.14074,arxiv:2306.17686}. The \([[105,1]]\) concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are transversal w.r.t. to two different partitions \cite{arxiv:1309.3310,arxiv:1710.07256}.'
+      detail: 'The \([[15,1,3]]\) code can be viewed as a (gauge-fixed) doubled color code obtained from the Steane code via the doubling transformation \cite{arxiv:1509.03239}. A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[15,1,3]]\) code \cite{arxiv:1304.3709,arxiv:1403.2734,arxiv:1703.03860,arxiv:2210.14074,arxiv:2306.17686}. An \([[105,1,3]]\) alternative concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are close to transversal \cite{arxiv:1309.3310,arxiv:1710.07256}.'
     - code_id: concatenated_steane
       detail: 'The \([[105,1]]\) concatenation of the \([[15,1,3]]\) and Steane codes allows for a universal gate set consisting of gates that are transversal w.r.t. to two different partitions \cite{arxiv:1309.3310,arxiv:1710.07256}.'
     - code_id: qubit_concatenated

codes/quantum/qudits_galois/stabilizer/qldpc/distance_balanced.yml

@@ -22,7 +22,7 @@ description: |
 
 features:
   decoders:
-    - 'Single-ancilla syndrome extraction circuits that, for the most part, preserve the \hyperref[topic:effective-distance]{effective distance} of weight-reduced qLDPC codes \cite{arxiv:2409.02193}. The distance balancing technique of Ref. \cite{arxiv:2004.07935} preserves \hyperref[topic:effective-distance]{effective distance} \cite{arxiv:2409.02193}.'
+    - 'The effective distance of single-ancilla syndrome extraction QLDPC code circuits can be preserved under weight reduction \cite{arxiv:2409.02193}. The distance balancing technique of Ref. \cite{arxiv:2004.07935} preserves the \hyperref[topic:effective-distance]{effective distance} of single-ancilla syndrome extraction circuits \cite{arxiv:2409.02193}.'
   fault_tolerance:
     - 'Single-ancilla syndrome extraction circuits that, for the most part, preserve the \hyperref[topic:effective-distance]{effective distance} of weight-reduced qLDPC codes \cite{arxiv:2409.02193}. The distance balancing technique of Ref. \cite{arxiv:2004.07935} preserves \hyperref[topic:effective-distance]{effective distance} \cite{arxiv:2409.02193}.'